Whakaoti i te 3x^2+5x=0

$$3 x ^ { 2 } + 5 x = 0$$

Whakaoti mō x

$$x = -\frac{5}{3} = -1\frac{2}{3} \approx -1.666666667$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

Tauwehea te x.

$$x\left(3x+5\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te 3x+5=0.

$$x=0 x=-\frac{5}{3}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Ko ngā whārite katoa o te āhua ax^{2}+bx+c=0 ka taea te whakaoti mā te whakamahi i te tikanga tātai pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. E rua ngā otinga ka puta i te tikanga tātai pūrua, ko tētahi ina he tāpiri a ±, ā, ko tētahi ina he tango.

$$3x^{2}+5x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 3 mō a, 5 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-5±\sqrt{5^{2}}}{2\times 3}$$

Tuhia te pūtakerua o te 5^{2}.

$$x=\frac{-5±5}{2\times 3}$$

Whakareatia 2 ki te 3.

$$x=\frac{-5±5}{6}$$

Nā, me whakaoti te whārite x=\frac{-5±5}{6} ina he tāpiri te ±. Tāpiri -5 ki te 5.

$$x=\frac{0}{6}$$

Whakawehe 0 ki te 6.

$$x=0$$

Nā, me whakaoti te whārite x=\frac{-5±5}{6} ina he tango te ±. Tango 5 mai i -5.

$$x=-\frac{10}{6}$$

Whakahekea te hautanga \frac{-10}{6} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x=-\frac{5}{3}$$

Kua oti te whārite te whakatau.

$$x=0 x=-\frac{5}{3}$$

Ngā Upane mō te Whakaoti i te Pūrua

Ko ngā whārite pūrua pēnei i tēnei nā ka taea te whakaoti mā te whakaoti i te pūrua. Hei whakaoti i te pūrua, ko te whārite me mātua tuhi ki te āhua x^{2}+bx=c.

$$3x^{2}+5x=0$$

Whakawehea ngā taha e rua ki te 3.

$$\frac{3x^{2}+5x}{3}=\frac{0}{3}$$

Mā te whakawehe ki te 3 ka wetekia te whakareanga ki te 3.

$$x^{2}+\frac{5}{3}x=\frac{0}{3}$$

Whakawehe 0 ki te 3.

$$x^{2}+\frac{5}{3}x=0$$

Whakawehea te \frac{5}{3}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{5}{6}. Nā, tāpiria te pūrua o te \frac{5}{6} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+\frac{5}{3}x+\left(\frac{5}{6}\right)^{2}=\left(\frac{5}{6}\right)^{2}$$

Pūruatia \frac{5}{6} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+\frac{5}{3}x+\frac{25}{36}=\frac{25}{36}$$

Tauwehea x^{2}+\frac{5}{3}x+\frac{25}{36}. Ko te tikanga pūnoa, ina ko x^{2}+bx+c he pūrua tika pūrua tika pū, ka taea taua mea te tauwehea i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{5}{6}\right)^{2}=\frac{25}{36}$$

Tuhia te pūtakerua o ngā taha e rua o te whārite.

$$\sqrt{\left(x+\frac{5}{6}\right)^{2}}=\sqrt{\frac{25}{36}}$$

Whakarūnātia.

$$x+\frac{5}{6}=\frac{5}{6} x+\frac{5}{6}=-\frac{5}{6}$$

Me tango \frac{5}{6} mai i ngā taha e rua o te whārite.

$$x=0 x=-\frac{5}{3}$$